Nonparametric Regression Procedures Research Articles

ESTIMATION OF A BI-RESPONSE TRUNCATED SPLINE NONPARAMETRIC REGRESSION MODEL ON LIFE EXPECTANCY AND PREVALENCE OF UNDERWEIGHT CHILDREN IN INDONESIA

Researchers use the nonparametric regression method because it provides excellent flexibility in the modeling process. Nonparametric regression procedures can be used if the relationship pattern between the predictor and response variables is unknown. The truncated spline method is one of the most frequently used nonparametric regression methods. A truncated spline is a polynomial slice with continuous segmented properties, and the resulting curve is relatively smooth. The advantage of truncated splines is that they can be used on data that experience behavior changes at specific intervals. The nonparametric spline truncated bi-response regression approach is used when one or more predictor variables affect the two response variables with the assumption that there is a correlation between the response variables. This study aimed to obtain the best spline truncated bi-response nonparametric regression model on life expectancy data and the prevalence of underweight children in Indonesia in 2021. The data used comes from the Central Bureau of Statistics and the Indonesian Ministry of Health. The optimal knot point selection method uses the Generalized Cross Validation (GCV) method. The results showed that the best model formed was obtained using three-knot points based on a minimum GCV value of 22.77 and a coefficient of determination of 99.58%.

Nonparametric Instrumental Regression with Two-Way Fixed Effects

Abstract This paper proposes a novel estimator for nonparametric instrumental regression while controlling for additive two-way fixed effects. In particular, the Landweber–Fridman regularization, to overcome the ill-posed inverse problem in the nonparametric instrumental regression procedure, is combined with the local-within two-ways fixed effect estimator presented by Lee, Y., D. Mukherjee, and A. Ullah. (2019. “Nonparametric Estimation of the Marginal Effect in Fixed-Effect Panel Data Models.” Journal of Multivariate Analysis 171: 53–67). Compared to other estimators in this context, an appealing feature is its flexible applicability with respect to different panel model specifications, i.e. models comprising either individual, temporal, or two-way fixed effects. The estimator’s performance is tested on simulated data, where a Monte Carlo study reveals good finite sample behaviour. Confidence intervals are provided by applying the wild bootstrap.

Nonparametric Prediction Distribution from Resolution-Wise Regression with Heterogeneous Data

Modeling and inference for heterogeneous data have gained great interest recently due to rapid developments in personalized marketing. Most existing regression approaches are based on the conditional mean and may require additional cluster information to accommodate data heterogeneity. In this article, we propose a novel nonparametric resolution-wise regression procedure to provide an estimated distribution of the response instead of one single value. We achieve this by decomposing the information of the response and the predictors into resolutions and patterns, respectively, based on marginal binary expansions. The relationships between resolutions and patterns are modeled by penalized logistic regressions. Combining the resolution-wise prediction, we deliver a histogram of the conditional response to approximate the distribution. Moreover, we show a sure independence screening property and the consistency of the proposed method for growing dimensions. Simulations and a real estate valuation dataset further illustrate the effectiveness of the proposed method.

L-Spline Interpolation for Differential Operators of Order 4 with Constant Coefficients


 
 
 In this paper it is shown that many features from polynomial spline methods used in nonparametric regression and smoothing procedures carry over to the class of L-splines where L is a linear differential operator of order 4 with constant coefficients. Special attention is given to the question whether an analogue of the Reinsch algorithm is valid and criteria are given such that the associated matrix R is strictly diagonal dominant
 
 

OPTIMAL BANDWIDTH SELECTION IN NONLINEAR COINTEGRATING REGRESSION

We study optimal bandwidth selection in nonparametric cointegrating regression where the regressor is a stochastic trend process driven by short or long memory innovations. Unlike stationary regression, the optimal bandwidth is found to be a random sequence which depends on the sojourn time of the process. All random sequences $h_{n}$ that lie within a wide band of rates as the sample size $n\rightarrow \infty $ have the property that local level and local linear kernel estimates are asymptotically normal, which enables inference and conveniently corresponds to limit theory in the stationary regression case. This finding reinforces the distinctive flexibility of data-based nonparametric regression procedures for nonstationary nonparametric regression. The present results are obtained under exogenous regressor conditions, which are restrictive but which enable flexible data-based methods of practical implementation in nonparametric predictive regressions within that environment.

Nonparametric depth and quantile regression for functional data

We investigate nonparametric regression methods based on spatial depth and quantiles when the response and the covariate are both functions. As in classical quantile regression for finite dimensional data, regression techniques developed here provide insight into the influence of the functional covariate on different parts, like the center as well as the tails, of the conditional distribution of the functional response. Depth and quantile based nonparametric regression methods are useful to detect heteroscedasticity in functional regression. We derive the asymptotic behavior of the nonparametric depth and quantile regression estimates, which depend on the small ball probabilities in the covariate space. Our nonparametric regression procedures are used to analyze a dataset about the influence of per capita GDP on saving rates for 125 countries, and another dataset on the effects of per capita net disposable income on the sale of cigarettes in some states in the US.

Efficient Blind Image Deblurring Using Nonparametric Regression and Local Pixel Clustering

ABSTRACTBlind image deblurring is a challenging ill-posed problem. It would have an infinite number of solutions even in cases when an observed image contains no noise. In reality, however, observed images almost always contain noise. The presence of noise would make the image deblurring problem even more challenging because the noise can cause numerical instability in many existing image deblurring procedures. In this article, a novel blind image deblurring approach is proposed, which can remove both pointwise noise and spatial blur efficiently without imposing restrictive assumptions on either the point spread function (psf) or the true image. It even allows the psf to be location dependent. In the proposed approach, a local pixel clustering procedure is used to handle the challenging task of restoring complicated edge structures that are tapered by blur, and a nonparametric regression procedure is used for removing noise at the same time. Numerical examples show that our proposed method can effectively handle a wide variety of blur and it works well in applications. Supplementary materials for this article are available online.

Multivariate Adaptive Regression Splines Application for Multivariate Geotechnical Problems with Big Data

Despite the rapid increases in processing speed and memory of low-cost computers, the enormous computational costs of running complicated numerical analyses such as finite element simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization since many geotechnical problems are highly nonlinear and multivariate. To reduce the cost, surrogate models, also known as meta-models, are constructed and then used in place of the actual numerical simulation models. To ensure the surrogate model is more reliable, the ranges of the design variables should be as wide as possible. Thus meta-modeling techniques capable of analyzing multivariate problems are desirable. This paper explores the use of a fairly simple nonparametric regression procedure known as multivariate adaptive regression splines (MARS) in approximating the relationship between the inputs and outputs with a big data. First the basis of the MARS methodology and its associated procedures are explained in detail. Then two complicated geotechnical problems are presented to demonstrate the function approximating capabilities of MARS and its efficiency in dealing with multivariate problems involving large amounts of data. This paper demonstrates that the MARS algorithm is capable of producing simple, accurate and easy-to-interpret models and estimating the contributions of the input variables.

Assessment of soil liquefaction based on capacity energy concept and multivariate adaptive regression splines

Soil liquefaction is one of the most complicated phenomena to assess in geotechnical earthquake engineering. The procedures that have been developed to determine the liquefaction potential of sandy soil deposits can be categorized into three main groups: stress-based, strain-based, and energy-based procedures. The main advantage of the energy-based approach over the other two methods is the fact that it considers the effects of strain and stress concurrently unlike the stress or strain-based methods. Several liquefaction evaluation procedures have been developed, relating the capacity energy to initial soil parameters such as the relative density, initial effective confining pressure, fine contents and soil textural properties. Analyses have been carried out on a total of 302 previously published tests using a nonparametric regression procedure known as multivariate adaptive regression splines (MARS), to assess the capacity energy required to trigger liquefaction in sand and silty sands. The capacity energies estimated by this proposed model compare favorably with the centrifuge test data sets used for validation purpose.

Inference on varying-coefficient partially linear regression model

The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. (2008) proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized likelihood ratio test is established. Under the null hypotheses the normalized test statistic follows a χ2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance parameters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.

Local comparison of empirical distributions via nonparametric regression

Given two independent samples of size n and m drawn from univariate distributions with unknown densities f and g, respectively, we are interested in identifying subintervals where the two empirical densities deviate significantly from each other. The solution is built by turning the nonparametric density comparison problem into a comparison of two regression curves. Each regression curve is created by binning the original observations into many small size bins, followed by a suitable form of root transformation to the binned data counts. Turned as a regression comparison problem, several nonparametric regression procedures for detection of sparse signals can be applied. Both multiple testing and model selection methods are explored. Furthermore, an approach for estimating larger connected regions where the two empirical densities are significantly different is also derived, based on a scale-space representation. The proposed methods are applied on simulated examples as well as real-life data from biology.

An improvement to MLR model for predicting liquefaction-induced lateral spread using multivariate adaptive regression splines

Soil liquefaction during earthquakes can result in ground movements that cause damage to buildings and lifelines. Lateral spreading is one form of earthquake-induced ground movements that have caused extensive damage in previous earthquakes. The lateral displacement is dependent on many factors including the earthquake magnitude, thickness and particle size of the liquefiable subsoils and the depth of the groundwater. A number of analytical and empirical methods have been proposed to predict the magnitude of the lateral displacement. One common empirical method is the MLR model which is based on multiple linear regression (MLR) analysis of a database of observed case histories. It is proposed in this paper to use a nonparametric regression procedure known as multivariate adaptive regression splines (MARS), as an improvement to the current MLR model to predict the liquefaction induced lateral displacement. First the basis of the MARS method and its associated procedures are explained in detail. Results are then presented to show the accuracy of the proposed approach, in comparison to the commonly used multiple regression approach. Analysis of observed case histories indicated that the MARS outperforms MLR in terms of predictive accuracy. MARS automatically models non-linearities and interactions between variables without making any specific assumptions. Furthermore, it is able to provide the relative importance of the input variables and give insights of where significant changes in the data may occur.

Nonparametric Regression With Basis Selection From Multiple Libraries

New nonparametric regression procedures called BSML (Basis Selection from Multiple Libraries) are proposed in this article for estimating a complex function by a linear combination of basis functions adaptively selected from multiple libraries. Different classes of basis functions are chosen to model various features of the function, for example, truncated constants can model change points in the function, while polynomial spline representers may be used to model smooth components. The generalized cross-validation (GCV) and covariance inflation criteria are used to balance goodness of fit and model complexity where the model complexity is estimated adaptively by either the generalized degrees of freedom or covariance penalty. The cross-validation (CV) method is also considered for model selection. Spatially adaptive regression and model selection in multivariate nonparametric regression will be used to illustrate the flexibility and efficiency of the BSML procedures. Extensive simulations show that the BSML procedures are more adaptive than some well-known existing nonparametric regression methods. Analyses of real datasets are used to illustrate the BSML procedures. This article has supplementary materials online.

Modelling of reservoir-induced earthquakes: a multivariate adaptive regression spline

This paper employs a multivariate adaptive regression spline (MARS) for the prediction of the maximum magnitude (M) of reservoir-induced earthquakes based on reservoir parameters. MARS is a non-parametric adaptive regression procedure. It has the capability to determine the important sequence of inputs for the output. The comprehensive parameter (E) and maximum reservoir depth (H) are used as inputs for the MARS. The developed MARS gives an equation for the prediction of M. A comparative study is carried out between the developed MARS and other models and the results show that the developed MARS is a robust model for the prediction of M.

Study of MEPDG Sensitivity Using Nonparametric Regression Procedures

AbstractBecause the new Mechanistic-Empirical Pavement Design Guide (MEPDG) includes numerous inputs, a sensitivity analysis using the Monte Carlo approach is not practical because it requires thousands of MEPDG runs. Instead, nonparametric regression procedures can be very useful to perform MEPDG sensitivity analysis. In this study, nonparametric regression procedures such as multivariate adaptive regression splines and gradient boosting machine are employed to identify inputs that contribute significantly to the outputs. Thirty inputs are used to randomly generate 750 input combinations by using Latin hypercube sampling. Using four-layer pavement geometry [two asphalt concrete (AC), base, and subgrade layers], simulations are run in MEPDG software to produce a time series of predicted distresses such as roughness, rutting, and cracking. Sensitivity analysis resulted in three groups of inputs to which the output is (1) highly sensitive, (2) moderately sensitive, and (3) minimally sensitive. Results show ...

Derivation of a pediatric growth curve for inferior vena caval diameter in healthy pediatric patients: brief report of initial curve development

BackgroundA validated tool has long been sought to provide clinicians with a uniform and accurate method to assess hydration status in the pediatric emergency medicine population. Outpatient clinicians use CDC height- and weight-based curves for the assessment of physical development. In hospital, daily weights provide objective data; however, these are usually not available at presentation.One of the most promising techniques for the rapid assessment of volume is ultrasound (US) to obtain an indexed inferior vena cava diameter (IVCDi); as previously described. Prior studies have focused on IVCDi in dehydrated patients and have shown that it provides accurate estimates of right atrial pressure and volume status. The objective of this study is to derive an IVC growth curve in healthy pediatric patients.MethodsProspective cohort design enrolled healthy children between the ages of 4 weeks and 20 years. Patients presenting with fever, illnesses, or diagnoses known to affect the volume will be excluded. All eligible patients under 21, who have provided self or parental written consent, will undergo a brief ultrasound to obtain transverse and long images of both the IVC and the aorta; all scans will be digitally saved. Image quality will be subjectively rated as poor, fair, or good based on wall clarity. Poor quality images will be recorded but may be omitted from our analysis. Five clinicians completed a 1-h introduction to IVC-US and ten supervised scans prior to enrollment. Still images will be measured in order to determine IVCDi in both transverse and longitudinal planes. To assess inter-rater reliability, in 10% of cases, two clinicians will complete scans. All study scans will be over-read by a fellowship-trained sonologist.IVCDi will be plotted independently as functions of age, gender, BMI, and aortic diameter. Within each group, means with means or medians with 95% CIs will be calculated. Following uni- and bivariate analyses and assessment for colinearity, a variety of parametric and nonparametric regression procedures will be conducted. The smoothed curves will be approximated using a modified LMS estimation procedure.ResultsData for the initial curve derivation includes 25 patients ranging from 13 months to 20 years (mean 102 months or 8.5 years). Sixty-five percent of patients were enrolled from the ED, while 35% were enrolled from well-child clinic visits. When evaluating the size of IVC as a function of time linear growth, increasing size was found to proportionately increase with age of patient in months.ConclusionsData suggest a linear correlation between IVC size and age. Such data, when plotted as a new growth curve, may allow clinicians to plot a patient's sonographic measurements in order to assess hydration health.

Multivariate adaptive regression spline applied to friction capacity of driven piles in clay

This article employs Multivariate Adaptive Regression Spline (MARS) for determination of friction capacity of driven piles in clay. MARS is non-parametric adaptive regression procedure. Pile length, pile diameter, effective vertical stress, and undrained shear strength are considered as input of MARS and the output of MARS is friction capacity. The developed MARS gives an equation for determination of <TEX>$f_s$</TEX> of driven piles in clay. The results of the developed MARS have been compared with the Artificial Neural Network. This study shows that the developed MARS is a robust model for prediction of <TEX>$f_s$</TEX> of driven piles in clay.

Recursively Imputed Survival Trees

We propose recursively imputed survival tree (RIST) regression for right-censored data. This new nonparametric regression procedure uses a novel recursive imputation approach combined with extremely randomized trees that allows significantly better use of censored data than previous tree-based methods, yielding improved model fit and reduced prediction error. The proposed method can also be viewed as a type of Monte Carlo EM algorithm, which generates extra diversity in the tree-based fitting process. Simulation studies and data analyses demonstrate the superior performance of RIST compared with previous methods.

Uplift capacity of suction caisson in clay using multivariate adaptive regression spline

This study adopts Multivariate Adaptive Regression Spline (MARS) model for determination of uplift capacity ( Q) of suction caisson in clay. MARS is a non-parametric adaptive regression procedure. The model inputs included the L/ d ( L is the embedded length of the caisson and d is the diameter of caisson), undrained shear strength of soil at the depth of the caisson tip ( s u), D/ L ( D is the depth of the load application point from the soil surface), inclined angle ( θ) and load rate parameter ( T k). The output of MARS is Q. The results of MARS are compared with Artificial Neural Network (ANN) and Finite Element Method (FEM). An equation has been presented from the developed MARS. The results show the strong potential of MARS to be applied to uplift capacity of suction caisson in clay.

Nonparametric regression in exponential families

Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In this paper we consider nonparametric regression in exponential families with the main focus on the natural exponential families with a quadratic variance function, which include, for example, Poisson regression, binomial regression and gamma regression. We propose a unified approach of using a mean-matching variance stabilizing transformation to turn the relatively complicated problem of nonparametric regression in exponential families into a standard homoscedastic Gaussian regression problem. Then in principle any good nonparametric Gaussian regression procedure can be applied to the transformed data. To illustrate our general methodology, in this paper we use wavelet block thresholding to construct the final estimators of the regression function. The procedures are easily implementable. Both theoretical and numerical properties of the estimators are investigated. The estimators are shown to enjoy a high degree of adaptivity and spatial adaptivity with near-optimal asymptotic performance over a wide range of Besov spaces. The estimators also perform well numerically.